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Search: Posts Made By: preda
Forum: Math 2020-08-13, 05:00
Replies: 3
Views: 198
Posted By preda
Yes. Fixing that, and changing the log() from...

Yes. Fixing that, and changing the log() from base 'e' to base 2, we get:
integral(1/x * rho((x - a)/b), x, N, infinity),
where a=log2(P), b=log2(B1). i.e. the integral has the nice property of...
Forum: Math 2020-08-12, 04:56
Replies: 3
Views: 198
Posted By preda
Help with a Dickman's Rho integral

Hi, could somebody help me approximate this integral:
(where rho() is Dickman's Rho function)

integral(rho((log(x)-log(p))/log(B1)) / (x*log(x)), x = 2^N to inf)

This is what I tried myself...
Forum: GpuOwl 2020-08-10, 02:56
Replies: 7
Views: 366
Posted By preda
Of course "optimal bounds" depends on the...

Of course "optimal bounds" depends on the "factored up to" bits. A first approximation for 100M exponents may be:
factored-to, B1, B2, chance
77: 1.2M 40M 4.2%
78: 1M 35M 3.6%
79: 1M 30M 3.2%...
Forum: GpuOwl 2020-08-07, 10:25
Replies: 7
Views: 366
Posted By preda
I am just revisiting the P-1 probabilities. ...

I am just revisiting the P-1 probabilities.

Based on my intuition (which is based on a few articles, among others...
Forum: GPU Computing 2020-08-06, 23:45
Replies: 344
Views: 20,260
Posted By preda
The PCIe does signaling at very high frequency,...

The PCIe does signaling at very high frequency, and that pushes the envelope of what the cable can do (within the noise margins). That's why I recommend "Always set PCIe to GEN-1 speeds in BIOS, and...
Forum: GpuOwl 2020-08-06, 08:23
Replies: 2,393
Views: 135,943
Posted By preda
It seems GpuOwl accepts the PRP line with the...

It seems GpuOwl accepts the PRP line with the cofactor present, but GpuOwl not being aware of or using the cofactor in any way may be sub-optimal. GpuOwl will simply run a classic PRP test, which...
Forum: Puzzles 2020-08-06, 06:14
Replies: 27
Views: 953
Posted By preda
Nice Robert, thank you! I look forward to...

Nice Robert, thank you! I look forward to implementing this, I have a feeling P-1 first-stage just got a speed boost :)

(disclaimer: when used in conjuction with PRP)
Forum: Data 2020-08-05, 19:03
Replies: 65
Views: 5,689
Posted By preda
What was the old software? (is it a bug in the...

What was the old software? (is it a bug in the software or a hardware problem? or, unlikely, a fake result)

What software are you using now, that is finding the factors?
Forum: GpuOwl 2020-08-05, 18:49
Replies: 2,393
Views: 135,943
Posted By preda
If you prefer perl, it shouldn't be too hard to...

If you prefer perl, it shouldn't be too hard to translate the python script to perl.

If you have a python or perl script, you can inspect it and see what it does. You can fix bugs or tweak the...
Forum: Puzzles 2020-08-04, 01:00
Replies: 27
Views: 953
Posted By preda
I broke through 718K: multiplying with...

I broke through 718K:
multiplying with 1999099*3684553 produces HW=717965

still a long way to go to 710K.. it looks like the "brute force search" is not working very well.
Forum: Puzzles 2020-08-03, 10:26
Replies: 27
Views: 953
Posted By preda
Is this a puzzle?

Consider the number PowerSmooth(1000000) with the 2 factors removed; e.g. in pari-gp:

PowerSmooth(B1)= result=1; forprime(p=3, B1, result *= p^floor(log(B1)/log(p))); return(result)...
Forum: Math 2020-08-03, 08:42
Replies: 22
Views: 738
Posted By preda
The Why

I'm going to give away the backstory for my question about low-hamming-weight multiples.

"It's all for P-1"

You may know, GpuOwl can do both PRP and P-1. PRP has the advantage of being...
Forum: Software 2020-08-03, 07:12
Replies: 581
Views: 74,389
Posted By preda
P-1 bounds getting lower too. A pity, I liked P-1...

P-1 bounds getting lower too. A pity, I liked P-1 :)

(I always thought P-1 is so much more beautiful than TF :), but TF is done early to high-bits and too little opportunity is left for P-1)
Forum: News 2020-08-03, 00:55
Replies: 281
Views: 12,501
Posted By preda
If you use gpuowl's primenet.py script with...

If you use gpuowl's primenet.py script with proofs it "just works". Also works great with multiple instances of gpuowl with -pool <dir> to gpuowl.

The proof files not-yet-uploaded are in the...
Forum: News 2020-08-02, 01:43
Replies: 281
Views: 12,501
Posted By preda
CERT self-verification (yes it's fine)

Yes the same person doing proof and CERT on the same exponent is fine. No weakness there.

PS: we should put together a FAQ on the new proof/cert thing. The above would be question No. 1 :)
Forum: News 2020-08-01, 23:54
Replies: 281
Views: 12,501
Posted By preda
The problem was not "string parsing in C", it's...

The problem was not "string parsing in C", it's the un-intuitive behavior of scanf() to keep consuming whitespace after any whitespace format character.
E.g. scanf("\n") will eat the newline *and*...
Forum: Number Theory Discussion Group 2020-08-01, 07:52
Replies: 13
Views: 626
Posted By preda
Hi Viliam, I'm by no means an LL expert, and I...

Hi Viliam, I'm by no means an LL expert, and I don't have an answer to your question here. However, I would approach the question by drilling down into one (or a few) mathematical proofs of the LL...
Forum: Soap Box 2020-07-30, 05:54
Replies: 70
Views: 1,284
Posted By preda
This line of discussion could form the basis of a...

This line of discussion could form the basis of a fascinating separate thread, IMO.
Forum: News 2020-07-30, 04:39
Replies: 281
Views: 12,501
Posted By preda
Alternativelly to using the shift count you could...

Alternativelly to using the shift count you could vary the "random" used to generate the CERT task.
Forum: Math 2020-07-30, 02:02
Replies: 22
Views: 738
Posted By preda
A simple information theoretic argument, based on...

A simple information theoretic argument, based on entropy, suggests that (almost all) numbers of N bits have a multiple of 2xN bits with a N/10 binary hamming weight (HW).

(below, log() is in base...
Forum: News 2020-07-30, 00:22
Replies: 281
Views: 12,501
Posted By preda
CERTs could (and should?) use the same GEC as the...

CERTs could (and should?) use the same GEC as the normal PRP iterations. This way the correctness of the CERT work can be verified locally (that's what GEC does) before sending the CERT result.
...
Forum: News 2020-07-30, 00:02
Replies: 281
Views: 12,501
Posted By preda
Yes, GpuOwl processing CERTs would be possible,...

Yes, GpuOwl processing CERTs would be possible, but is that necessary or useful? I think the whole supply of CERT work that we can expect in the future can be easily handled by mprime.

Also, CERTs...
Forum: Math 2020-07-29, 08:11
Replies: 22
Views: 738
Posted By preda
Thanks! How would solving the discrete log look...

Thanks!
How would solving the discrete log look like for:
3 * 5 * 7 * 11 * 13 * 17 * 19 * 23 == 111546435
or for:
3 * 5 * 7 * 11 * 13 * 17 * 19 * 23 * 27 == 3011753745
?

Let's say we want a...
Forum: GpuOwl 2020-07-28, 13:32
Replies: 13
Views: 661
Posted By preda
primenet.py and upload.py scripts for proof upload

The proof upload in GpuOwl has been improved in a recent commit:
https://github.com/preda/gpuowl/commit/f887d6e74015c17429fb96e65d3d8b65cb7657a1

Previously the upload data used an inefficient...
Forum: Math 2020-07-28, 11:23
Replies: 22
Views: 738
Posted By preda
Yes indeed. There are the categories of "sturdy...

Yes indeed. There are the categories of "sturdy numbers" and the opposite of "flimsy numbers". see e.g. https://oeis.org/A125121
Showing results 1 to 25 of 1000

 
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